Observations about the universe, life, Lausanne and me

Tuesday, January 19, 2010

Vector calculus in curvilinear coordinates

Quick heads-up: If you are looking into delving into vector calculus, and want to calculate the gradient in orthogonal curvilinear coordinate systems, do not start with

is the ath partial derivative in curvilinear coordinates, Ac a vector and êc a basis vector.
because that resolves to (after many headaches, deriving the derivatives of basis vectors and general cursing):

where ha would be the Lamé-coefficients of the specific basis. This is the expression for the gradient of a vector-field, not a scalar field, which should not come as a surprise of course, since (Acêc) is a vector.

Should not come as a surprise. Surprised the hell out of me, though.

Apparently I have nearly managed to forget everything I ever learned about vector and tensor calculus - so I know what I will be doing the next couple of days...

Edit: Formulas generated via the excellent Texify webpage. If you can't see any, then Texify is dead or down - sorry about that!

Edit the second: Put in the formulas as images, so everybody can see them, even if Texify is acting up - thanks Stephanie for pointing that out!.


  1. Catchy title, you wild man, you. Nothing gets a girl all excited like curvilinear coordinates.


    I couldn't see the formulas, but, let's face it, I haven't done math like that in decades. If I saw it, I would only be humiliated.

  2. This comment has been removed by a blog administrator.

  3. I know Stephanie - something I'll try at the next party for sure! Nothing beats 'May I do vector calculus on your curvilinear coordinate system' for a pick-up line ;)

    Btw, I fixed the formulas, if you want to bask in the glory that is the gradient of a vector-field.

  4. Not that I'm not fond of you, Boris, but I really don't.